This collection of papers is dedicated to the memory of Gaetano Fichera, a great mathematician and also a good friend to the editors. Regrettably it took an unusual amount of time to bring this collection out. This was primarily due to the fact that the main editor who had collected all of the materials, for this volume, P. D. Panagiotopoulos, died unexpectedly during the period when we were editing the manuscript. The other two editors in appreciation of Panagiotopoulos' contribution to this field, believe it is therefore fitting that this collection be dedicated to his memory also. The theme of the collection is centered around the seminal research of G. Fichera on the Signorini problem. Variants on this idea enter in different ways. For example, by bringing in friction the problem is no longer self-adjoint and the minimization formulation is not valid. A large portion of this collection is devoted to survey papers concerning hemivariational methods, with a main point of its application to nonsmooth mechanics. Hemivariational inequali ties, which are a generalization of variational inequalities, were pioneered by Panagiotopoulos. There are many applications of this theory to the study of non convex energy functionals occurring in many branches of mechanics. An area of concentration concerns contact problems, in particular, quasistatic and dynamic contact problems with friction and damage. Nonsmooth optimization methods which may be divided into the main groups of subgradient methods and bundle methods are also discussed in this collection."

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This book presents a self-contained introduction to the physics of computing, by addressing the fundamental underlying principles that involve the act of computing, regardless of the actual machine that is used to compute. Questions like "what is the minimum energy required to perform a computation?", "what is the ultimate computational speed that a computer can achieve?" or "how long can a memory last", are addressed here, starting from basic physics principles. The book is intended for physicists, engineers, and computer scientists, and it is designed for self-study by researchers who want to enter the field or as the main text for a one semester course at advanced undergraduate or graduate level. The theoretical concepts presented in this book are systematically developed from the very beginning, which only requires basic knowledge in physics and mathematics.

"Now, however, weface an Age of Discontinuity in world economy and tech- nology. We might succeed in making it an age of great economic growth as weil. But the one thing that is certain so far is that it will be a period of change-in technology and in economic policy, in industry structures and in economic theo- ry, in the knowledge needed to govern and manage, and in economic issues. While we have been busy finishing the great nineteenth-century economic ed- ijice, the foundations have shifted beneath our feet." Peter F. Drucker, 1968 The A~e Qf DiscQntinuity, p. 10 This project has had a lQng gestatiQn period, probably ultimately dating to a YQuthful QbsessiQn with watershed divides and bQundaries. My awareness Qf the problem Qf discQntinuity in eCQnQmics dates tQ my first enCQunter with the capi- tal theQry paradQxes in the late 1960s, the fruits Qf which can be seen in Chapter 8 Qf this book. This awareness led tQ a frostratiQn Qver the apparent lack Qf a mathematics Qf discQntinuity, a lack that was in the process of rapidly being QverCQme at that time.

This book on canonical duality theory provides a comprehensive review of its philosophical origin, physics foundation, and mathematical statements in both finite- and infinite-dimensional spaces. A ground-breaking methodological theory, canonical duality theory can be used for modeling complex systems within a unified framework and for solving a large class of challenging problems in multidisciplinary fields in engineering, mathematics, and the sciences. This volume places a particular emphasis on canonical duality theory's role in bridging the gap between non-convex analysis/mechanics and global optimization. With 18 total chapters written by experts in their fields, this volume provides a nonconventional theory for unified understanding of the fundamental difficulties in large deformation mechanics, bifurcation/chaos in nonlinear science, and the NP-hard problems in global optimization. Additionally, readers will find a unified methodology and powerful algorithms for solving challenging problems in complex systems with real-world applications in non-convex analysis, non-monotone variational inequalities, integer programming, topology optimization, post-buckling of large deformed structures, etc. Researchers and graduate students will find explanation and potential applications in multidisciplinary fields.

Fads are as common in mathematics as in any other human activity, and it is always difficult to separate the enduring from the ephemeral in the achievements of one's own time. An unfortunate effect of the predominance of fads is that if a student doesn't learn about such worthwhile topics as the wave equation, Gauss's hypergeometric function, the gamma function, and the basic problems of the calculus of variations-among others-as an undergraduate, then he/she is unlikely to do so later. The natural place for an informal acquaintance with such ideas is a leisurely introductory course on differential equations. Specially designed for just such a course, Differential Equations with Applications and Historical Notes takes great pleasure in the journey into the world of differential equations and their wide range of applications. The author-a highly respected educator-advocates a careful approach, using explicit explanation to ensure students fully comprehend the subject matter. With an emphasis on modeling and applications, the long-awaited Third Edition of this classic textbook presents a substantial new section on Gauss's bell curve and improves coverage of Fourier analysis, numerical methods, and linear algebra. Relating the development of mathematics to human activity-i.e., identifying why and how mathematics is used-the text includes a wealth of unique examples and exercises, as well as the author's distinctive historical notes, throughout. Provides an ideal text for a one- or two-semester introductory course on differential equations Emphasizes modeling and applications Presents a substantial new section on Gauss's bell curve Improves coverage of Fourier analysis, numerical methods, and linear algebra Relates the development of mathematics to human activity-i.e., identifying why and how mathematics is used Includes a wealth of unique examples and exercises, as well as the author's distinctive historical notes, throughout Uses explicit explanation to ensure students fully comprehend the subject matter Outstanding Academic Title of the Year, Choice magazine, American Library Association.

This book describes the solution of electrodynamic boundary problems, which arose in the practical life of a designer. Only a few problems can be solved analytically and some of these solutions are given in the book, for example, the computation of a strip line in a rectangular or circular cylinder capacitance. Practical lines' configurations require computational work. As the authors' practice shows, the use of Green functions, leading to singular integral equations, is a powerful and pretty universal method to solve different boundary problems, including electrodynamic ones. The book presents the results of computations of microstrip lines on magnetized (longitudinally and transversally) ferrite and semiconductor substrates taking into account all the geometric sizes. The properties of gyrotropic media are described in the book for the reader's convenience. The geometrical shape may be practically any. The integral equations are exact and give the proper field near the edges. Actually, the use of singular integral equations reduces the experimental verification to minimum. The book will be useful for students, engineers, designers and researchers. It contains a lot of computed results, which are verified experimentally and can be used immediately.

This two-volume work introduces the theory and applications of Schur-convex functions. The first volume introduces concepts and properties of Schur-convex functions, including Schur-geometrically convex functions, Schur-harmonically convex functions, Schur-power convex functions, etc. and also discusses applications of Schur-convex functions in symmetric function inequalities.

The study of wall-bounded turbulent ows is of considerable interest from both scienti c and practical view points. As such it has attracted a great deal of research over the last 100 years. Much research has concentratedon ows over smooth walls since these are simpler from experimental, numerical and theoretical standpoints. The ow over rough walls has still received considerable attention but progress has necessarilybeenslower.Perhapsthemostessentialproblem(certainlyfromaprac- cal point of view) is to be able to predict the skin-frictiondrag acting on a plate (or a body) given a certain known roughness characteristic of the surface. Unfortunately this has proved to be very dif cult since even the simplest rough surfaces can be characterised by a number of different parameters and we still cannot directly c- nectthese tothe uiddynamicdragin a givensituation.Varioustheoriesandmodels have been proposed in order to make progress but there is still some disagreement in the community as to the correct understanding of these important ows.

This monograph is devoted to the creation of a comprehensive formalism for quantitative description of polarized modes' linear interaction in modern single-mode optic fibers. The theory of random connections between polarized modes, developed in the monograph, allows calculations of the zero shift deviations for a fiber ring interferometer. The monograph addresses also the Sagnac effect and the Thomas precession. Devices such as gyroscopes, used in navigation and flight control, work based on this technology. Given the ever increasing market for navigation and air traffic, researchers and practitioners in research and industry need a fundamental and sound understanding of the principles. This work presents the underlying physical foundations.

This dissertation focuses on the calculation of transport coefficients in the matter created in a relativistic heavy-ion collision after chemical freeze-out. This matter can be well approximated using a pion gas out of equilibrium. We describe the theoretical framework needed to obtain the shear and bulk viscosities, the thermal and electrical conductivities and the flavor diffusion coefficients of a meson gas at low temperatures. To describe the interactions of the degrees of freedom, we use effective field theories with chiral and heavy quark symmetries. We subsequently introduce the unitarization methods in order to obtain a scattering amplitude that satisfies the unitarity condition exactly, then go on to calculate the transport properties of the low-temperature phase of quantum chromodynamics - the hadronic medium - which can be used in hydrodynamic simulations of a relativistic heavy-ion collision and its subsequent evolution. We show that the shear viscosity over entropy density exhibits a minimum in a phase transition by studying this coefficient in atomic Argon (around the liquid-gas phase transition) and in the linear sigma model in the limit of a large number of scalar fields (which presents a chiral phase transition). Finally, we provide an experimental method for estimating the bulk viscosity in relativistic heavy-ion collisions by performing correlations of the fluctuating components of the stress-energy tensor.

Convex Analysis may be considered as a refinement of standard calculus, with equalities and approximations replaced by inequalities. As such, it can easily be integrated into a graduate study curriculum. Minimization algorithms, more specifically those adapted to non-differentiable functions, provide an immediate application of convex analysis to various fields related to optimization and operations research. These two topics making up the title of the book, reflect the two origins of the authors, who belong respectively to the academic world and to that of applications. Part I can be used as an introductory textbook (as a basis for courses, or for self-study); Part II continues this at a higher technical level and is addressed more to specialists, collecting results that so far have not appeared in books.

This textbook, designed for a single semester course, begins with basic set theory, and moves briskly through fundamental, exponential, and logarithmic functions. Limits and derivatives finish the preparation for economic applications, which are introduced in chapters on univariate functions, matrix algebra, and the constrained and unconstrained optimization of univariate and multivariate functions. The text finishes with chapters on integrals, the mathematics of finance, complex numbers, and differential and difference equations.

Rich in targeted examples and explanations, Mathematical Economics offers the utility of a handbook and the thorough treatment of a text. While the typical economics text is written for two semester applications, this text is focused on the essentials. Instructors and students are given the concepts in conjunction with specific examples and their solutions.

Pulsed-Power Systems describes the physical and technical foundations for the production and application of high-voltage pulses of very high-power and high-energy character. In the initial chapters, it addresses materials, components and the most common diagnostics. In the second part, three categories of applications with scientific and industrial relevance are detailed: production of strong pulsed electric and magnetic fields, intense radiation sources and pulsed electric (plasma) discharges.

STRUCTURAL ANALYSIS WITH THE FINITE ELEMENT METHOD

Linear Statics

Volume 1: The Basis and Solids

Eugenio Onate

The two volumes of this book cover most of the theoretical and computational aspects of the linear static analysis of structures with the Finite Element Method (FEM). The content of the book is based on the lecture notes of a basic course on Structural Analysis with the FEM taught by the author at the Technical University of Catalonia (UPC) in Barcelona, Spain for the last 30 years.

Volume1 presents the basis of the FEM for structural analysis and a detailed description of the finite element formulation for axially loaded bars, plane elasticity problems, axisymmetric solids and general three dimensional solids. Each chapter describes the background theory for each structural model considered, details of the finite element formulation and guidelines for the application to structural engineering problems. The book includes a chapter on miscellaneous topics such as treatment of inclined supports, elastic foundations, stress smoothing, error estimation and adaptive mesh refinement techniques, among others. The text concludes with a chapter on the mesh generation and visualization of FEM results.

The book will be useful for students approaching the finite element analysis of structures for the first time, as well as for practising engineers interested in the details of the formulation and performance of the different finite elements for practical structural analysis.

STRUCTURAL ANALYSIS WITH THE FINITE ELEMENT METHOD

Linear Statics

Volume 2: Beams, Plates and Shells

Eugenio Onate

The two volumes of this book cover most of the theoretical and computational aspects of the linear static analysis of structures with the Finite Element Method (FEM).The content of the book is based on the lecture notes of a basic course on Structural Analysis with the FEM taught by the author at the Technical University of Catalonia (UPC) in Barcelona, Spain for the last 30 years.

Volume 2 presents a detailed description of the finite element formulation for analysis of slender and thick beams, thin and thick plates, folded plate structures, axisymmetric shells, general curved shells, prismatic structures and three dimensional beams. Each chapter describes the background theory for each structural model considered, details of the finite element formulation and guidelines for the application to structural engineering problems Emphasis is put on the treatment of structures with layered composite materials.

The book will be useful for students approaching the finite element analysis of beam, plate and shell structures for the first time, as well as for practising engineers interested in the details of the formulation and performance of the different finite elements for practical structural analysis.

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This volume comprises both research and survey articles originating from the conference on Arithmetic and Geometry around Quantization held in Istanbul in 2006. A wide range of topics related to quantization are covered, thus aiming to give a glimpse of a broad subject in very different perspectives.

This textbook effectively builds a bridge from basic number theory to recent advances in applied number theory. It presents the first unified account of the four major areas of application where number theory plays a fundamental role, namely cryptography, coding theory, quasi-Monte Carlo methods, and pseudorandom number generation, allowing the authors to delineate the manifold links and interrelations between these areas. Number theory, which Carl-Friedrich Gauss famously dubbed the queen of mathematics, has always been considered a very beautiful field of mathematics, producing lovely results and elegant proofs. While only very few real-life applications were known in the past, today number theory can be found in everyday life: in supermarket bar code scanners, in our cars' GPS systems, in online banking, etc. Starting with a brief introductory course on number theory in Chapter 1, which makes the book more accessible for undergraduates, the authors describe the four main application areas in Chapters 2-5 and offer a glimpse of advanced results that are presented without proofs and require more advanced mathematical skills. In the last chapter they review several further applications of number theory, ranging from check-digit systems to quantum computation and the organization of raster-graphics memory. Upper-level undergraduates, graduates and researchers in the field of number theory will find this book to be a valuable resource.

Theory of Nonlinear Propagation of High Harmonics Generated in a Gaseous Medium establishes the theoretical tools to study High-Order Harmonic Generation (HHG) by intense ultrafast infrared lasers in atoms and molecules. The macroscopic propagation of both laser and high-harmonic fields is taken into account by solving Maxwell's wave equations, while the single-atom or single-molecule response is treated with a quantitative rescattering theory by solving the time-dependent Schroedinger equation. This book demonstrates for the first time that observed experimental HHG spectra of atoms and molecules can be accurately reproduced theoretically when precise experimental conditions are known. The macroscopic HHG can be expressed as a product of a macroscopic wave packet and a photorecombination cross section, where the former depends on laser and experimental conditions while the latter is the property of target atoms or molecules. The factorization makes it possible to retrieve microscopically atomic or molecular structure information from the measured macroscopic HHG spectra. This book also investigates other important issues about HHG, such as contributions from multiple molecular orbitals, the minimum in the HHG spectrum, the spatial mode of laser beams, and the generation of an isolated attosecond pulse. Additionally, this book presents the photoelectron angular distribution of aligned molecules ionized by the HHG light.

In the modern world of gigantic datasets, which scientists and practioners of all fields of learning are confronted with, the availability of robust, scalable and easy-to-use methods for pattern recognition and data mining are of paramount importance, so as to be able to cope with the avalanche of data in a meaningful way. This concise and pedagogical research monograph introduces the reader to two specific aspects - clustering techniques and dimensionality reduction - in the context of complex network analysis. The first chapter provides a short introduction into relevant graph theoretical notation; chapter 2 then reviews and compares a number of cluster definitions from different fields of science. In the subsequent chapters, a first-principles approach to graph clustering in complex networks is developed using methods from statistical physics and the reader will learn, that even today, this field significantly contributes to the understanding and resolution of the related statistical inference issues. Finally, an application chapter examines real-world networks from the economic realm to show how the network clustering process can be used to deal with large, sparse datasets where conventional analyses fail.

Continuing the theme of the first, this second volume continues the study of the uses and techniques of numerical experimentation in the solution of PDEs. It includes topics such as initial-boundary-value problems, a complete survey of theory and numerical methods for conservation laws, and numerical schemes for elliptic PDEs. The author stresses the use of technology and graphics throughout for both illustration and analysis.

Quantum field theory has been a great success for physics, but it is difficult for mathematicians to learn because it is mathematically incomplete. Folland, who is a mathematician, has spent considerable time digesting the physical theory and sorting out the mathematical issues in it. Fortunately for mathematicians, Folland is a gifted expositor. The purpose of this book is to present the elements of quantum field theory, with the goal of understanding the behavior of elementary particles rather than building formal mathematical structures, in a form that will be comprehensible to mathematicians. Rigorous definitions and arguments are presented as far as they are available, but the text proceeds on a more informal level when necessary, with due care in identifying the difficulties. The book begins with a review of classical physics and quantum mechanics, then proceeds through the construction of free quantum fields to the perturbation-theoretic development of interacting field theory and renormalization theory, with emphasis on quantum electrodynamics. The final two chapters present the functional integral approach and the elements of gauge field theory, including the Salam-Weinberg model of electromagnetic and weak interactions.

This book introduces the basic concepts and methods that are useful in the statistical analysis and modeling of the DNA-based marker and phenotypic data that arise in agriculture, forestry, experimental biology, and other fields. It concentrates on the linkage analysis of markers, map construction and quantitative trait locus (QTL) mapping, and assumes a background in regression analysis and maximum likelihood approaches. The strength of this book lies in the construction of general models and algorithms for linkage analysis, as well as in QTL mapping in any kind of crossed pedigrees initiated with inbred lines of crops.

This volume contains survey and original articles presenting the state of the art on the application of GrAbner bases in control theory and signal processing. The contributions are based on talks delivered at the Special Semester on GrAbner Bases and Related Methods at the Johann Radon Institute of Computational and Applied Mathematics (RICAM), Linz, Austria, in May 2006.

Imagine mathematics, imagine with the help of mathematics, imagine new worlds, new geometries, new forms. This bookis intended to contribute to grasping how much that is interesting and new is happening in the relationships between mathematics, imagination and culture. With a look at the past, at figures and events, that help to understand the phenomena of today.

It is no coincidence that this volume contains an homage to the great Italian artist of the 1700s, Andrea Pozzo, and his perspective views. Theatre, art and architecture are the topics of choice, along with music, literature and cinema. No less important are applications of mathematics to medicine and economics.

The treatment is rigorous but captivating, detailed but full of evocations, an all-embracing look at the world of mathematics and culture

Today, a major component of any project management effort is the combined use of qualitative and quantitative tools. While publications on qualitative approaches to project management are widely available, few project management books have focused on the quantitative approaches. This book represents the first major project management book with a practical focus on the quantitative approaches to project management. The book organizes quantitative techniques into an integrated framework for project planning, scheduling, and control. Numerous illustrative examples are presented. Topics covered in the book include PERT/CPM/PDM and extensions, mathematical project scheduling, heuristic project scheduling, project economics, statistical data analysis for project planning, computer simulation, assignment and transportation problems, and learning curve analysis. Chapter one gives a brief overview of project management, presenting a general-purpose project management model. Chapter two covers CPM, PERT, and PDM network techniques. Chapter three covers project scheduling subject to resource constraints. Chapter four covers project optimization. Chapter five discusses economic analysis for project planning and control. Chapter six discusses learning curve analysis. Chapter seven covers statistical data analysis for project planning and control. Chapter eight presents techniques for project analysis and selection. Tables and figures are used throughout the book to enhance the effectiveness of the discussions. This book is excellent as a textbook for upper-level undergraduate and graduate courses in Industrial Engineering, Engineering Management, and Business, and as a detailed, comprehensive guidefor corporate management.